an open box made from a rectangular cardboard of sides 35cm and 20 cm by cutting the equal squares from each corner and then bending up the edges. if base area of box thus formed is 250 sq. cm find the length of the sides of the square cut from each corner
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Answer:
Step-by-step explanation:
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length of the sides of the square cut from each corner = 5 cm
Step-by-step explanation:
an open box made from a rectangular cardboard of sides 35cm and 20 cm by cutting the equal squares from each corner
Let say square cut from corners = d * d cm
Then sides of base = 35 - 2x & 20 - 2x
Area = (35 - 2x)(20 - 2x) = 250
=> (35 - 2x)(10 - x) = 125
=> 350 + 2x² - 20x - 35x = 125
=> 2x² - 55x + 225 = 0
=> 2x² - 10x - 45x + 225 = 0
=> 2x(x - 5) - 45(x - 5) = 0
=> (2x - 45) (x - 5) = 0
=> x = 45/2 or x = 5
2x < 20 => x ≠ 45/2
Hence x = 5
length of the sides of the square cut from each corner = 5 cm
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